@article{13672b01d764447ead9babcf5654538b,

title = "Steiner triple systems with high chromatic index",

abstract = "It has been conjectured that every Steiner triple system of order v 6= 7 has chromatic index at most (v + 3)=2 when v = 3 (mod 6) and at most (v + 5)=2 when v = 1 (mod 6). Herein, we construct a Steiner triple system of order v with chromatic index at least (v + 3)=2 for each integer v = 3 (mod 6) such that v ≥ 15, with four possible exceptions. We further show that the maximum number of disjoint parallel classes in the systems constructed is sublinear in v. Finally, we establish for each order v ≥ 15 (mod 18) that there are at least vv2(1=6+o(1)) nonisomorphic Steiner triple systems with chromatic index at least (v + 3)=2 and that some of these systems are cyclic.",

keywords = "Block coloring, Chromatic index, Parallel class, Steiner triple system",

author = "Darryn Bryant and Charles Colbourn and Daniel Horsley and Wanless, {Ian M.}",

note = "Funding Information: ∗Received by the editors January 31, 2017; accepted for publication (in revised form) July 25, 2017; published electronically November 14, 2017. http://www.siam.org/journals/sidma/31-4/M111433.html Funding: This work was supported by the Australian Research Council via grants DP150100530, DP150100506, DP120100790, and DE120100040 and by the National Science Foundation via grant 1421058. †School of Mathematics and Physics, The University of Queensland, St. Lucia, Qld, Australia (db@maths.uq.edu.au). ‡School of Computing, Informatics, and Decision Systems Engineering, Arizona State University, Tempe, AZ 85287 (Charles.Colbourn@asu.edu). §School of Mathematical Sciences, Monash University, Clayton, Victoria, Australia (danhorsley@ gmail.com, ian.wanless@monash.edu). Funding Information: This work was supported by the Australian Research Council via grants DP150100530, DP150100506, DP120100790, and DE120100040 and by the National Science Foundation via grant 1421058. Publisher Copyright: {\textcopyright} 2017 Society for Industrial and Applied Mathematics.",

year = "2017",

doi = "10.1137/17M1114338",

language = "English (US)",

volume = "31",

pages = "2603--2611",

journal = "SIAM Journal on Discrete Mathematics",

issn = "0895-4801",

publisher = "Society for Industrial and Applied Mathematics Publications",

number = "4",

}